This invention relates in general to devices and processes for reducing the amount of quantized data required to faithfully reproduce a sinusoidal signal over a range of frequencies, and in particular to such devices and processes in a direct-digital frequency synthesizer which uses quantized samples of the signal produced from summations of values stored in multiple sample memories.
The process used in conventional direct-digital frequency synthesizers is to communicate the output (phase) of a clocked, variable-increment, phase accumulator to a memory wherein quantized samples of the function being synthesized are mapped, i.e. stored in order of recall. The digital data from the memory is converted to corresponding analog signals which are then suitably filtered to remove high frequencies components inherently introduced by the process. Such a process is a general process for producing a wide variety of functions, e.g., sine, sawtooth, square wave, etc. Also, if the function being produced has symmetry, it is common to take advantage of the symmetry by mapping into the memory only that portion of the function which repeats itself for the purpose of reducing the amount of memory needed. For example, only a quadrant of a sine function, that is, 90 degrees, need be mapped because the other quadrants can be generated by simple digital manipulation. This process saves about 75% of the memory otherwise required.
This invention has the very significant advantage of allowing a further reduction in the amount of memory required for phase to sine wave conversion/transformation; the reduction can be by over 90% of the memory otherwise required. For example, in order to conventionally map magnitude samples of a sine function singularly corresponding to the phase outputs of a fourteen-bit phase accumulator (M=14) into a sample memory having a twelve-bit resolution output (K=12), one needs 2.sup.M .times.K bits of memory, which calculates to 196,608 bits, i.e. 16,384 quantized samples stored each as a twelve-bit binary number. For low and moderate speed operations, such large memories with suitable access times are available, but they are not currently available for high speed operations, e.g., over 50 Mhz. This invention can accomplish the same task, i.e., produce up to 2.sup.12 twelve-bit quantized samples, but only requires about 3152 bits of sample memory (in the preferred embodiment as discussed herein), a memory size that can be currently achieved for such high speed applications.
Heretofore, no direct-digital synthesizing device or process has been presented which takes advantage of characteristics of a sine wave as does this invention. This invention goes further and takes advantage of the smooth, monotonic, convex (albeit non-linear) properties of the sine wave. It uses piece-wise linear extrapolation and manipulation possible because of certain mathematical properties as will be explained.
A further advantage of this invention lies in the fact that the sample memories need not output data words wider than eight binary bits. From the standpoint of manufacturing integrated devices, this is very advantageous.
Other advantages and attributes of this invention will be readily discernible upon a reading of the text herein.